X+y+z=1
-2x+4y+6z=2
-x+3y-5z=11
solved using elimination

x = 0

y = 2

z = -1

Step-by-step explanation:

The system of equations are

x+y+z=1 - - - - - - - - - - 1

-2x+4y+6z=2 - - - - - - - - - 2

-x+3y-5z=11 - - - - - - - - - 3

Step 1

We would eliminate x by adding equation 1 to equation 3. It becomes

4y -4z = 12 - - - - - - - - - 4

Step 2

We would multiply equation 1 by 2. It becomes

2x + 2y + 2z = 2 - - - - - - - - - 5

We would add equation 2 and equation 5. It becomes

6y + 8z = 4 - - - - - - - - - 6

Step 3

We would multiply equation 4 by 6 and equation 6 by 4. It becomes

24y - 24z = 72 - - - - - - - - 7

24y + 32z = 16 - - - - - - - - 8

We would subtract equation 8 from equation 7. It becomes

-56z = 56

z = -56/56 = -1

Substituting z = -1 into 7, it becomes

24y - 24×-1 = 72

24y + 24 = 72

24y = 72 - 24 = 48

y = 48/24 = 2

Substituting y = 2 and z = -1 into equation 1, it becomes

x + 2 - 1 = 1

x = 1 - 1 = 0